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Imagine a third particle, which we will call a cyberon. It has three times the mass of an electron (3m). It has a positive charge that is three times the magnitude (3qe) of the charge on an electron. What is the ratio of the speed vc that the cyberon would have when it reaches the upper plate after being released from rest at position h0 to the speed ve that the electron would have

2 Answers

8 votes

Final answer:

In Physics, when comparing a hypothetical particle called cyberon to an electron, both released from rest and subject to the same electric potential difference, the ratio of their speeds upon reaching the upper plate would be 1. This implies that the cyberon and the electron would reach the plate at the same speed due to the mass and charge of the cyberon being three times that of the electron, which allows these factors to cancel each other out.

Step-by-step explanation:

The student has asked about the speed of a hypothetical particle named cyberon compared to the speed of an electron when both are released from the same height and reach an upper plate. This concept falls under the domain of Physics and involves principles such as electric potential energy, kinetic energy, and the mass-charge relationship of particles in an electric field.

To find out the ratio of the speeds, we would need to consider the work done by the electric field on both the electron and the cyberon, and apply the principle of conservation of energy. For a particle with charge q and mass m accelerating from rest due to an electric potential V, its final kinetic energy KE can be calculated using the equation KE = qV. The speed v of the particle is then found using the formula KE = 1/2 m v2.

For the electron:

KEe = qeV

ve = √(2qeV/me)

For the cyberon:

KEc = 3qeV (since the charge is three times that of the electron)

vc = √(2×3qeV/3me) = √(2qeV/me) (the mass is also three times that of the electron, so it cancels out)

Interestingly, the ratio of the speeds (vc/ve) would be:

vc / ve = 1

Meaning, both the cyberon and the electron would reach the upper plate at the same speed if they both started from rest and were subject to the same electric potential difference.

User Djibril
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4 votes

Answer:

Step-by-step explanation:

Let the potential difference between plate be V .

Electrical energy lost for cyberon = V x 3e

Kinetic energy lost by cyberon = kinetic energy gain by it

V x 3e = 1/2 x 3m x vc²

For electron , the above equation becomes

V x e = 1/2 x m x ve²

Dividing the two equations

1 = vc² / ve²

vc = ve .

vc / ve = 1 .

User TSK
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6.5k points